Question

A train moving at a speed of $220\,ms^{-1}$ towards a stationary object, emits a sound of frequency $1000\, Hz$. Some of the sound reaching the object gets reflected back to the train as echo. The frequency of the echo as detected by the driver of the train is (Speed of sound in air is $330\,ms^{-1}$)

• A. 3500 Hz
• B. 4000 Hz
• C. 5000 Hz
• D. 3000 Hz

Answer 1

Answer: (C)

5000 Hz

Answer 2

Here,
Speed of the train, $\upsilon_r = 220 \,ms ^{-1}$
Speed of sound in air, $\upsilon=330 \,ms^{-1}$
The frequency of the echo detected by the driver of the train is
$\upsilon'=\upsilon\Bigg(\frac{\upsilon+\upsilon_r}{\upsilon-\upsilon_r}\Bigg)=1000\Bigg(\frac{330+220}{330-220}\Bigg)$
$=1000\times\frac{550}{110}=5000 \,Hz$